Details

sample95.0ms

Algorithm

intervals

Results

43.0ms	258×	body	80	valid
8.0ms	8×	body	1280	valid
3.0ms	5×	body	320	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid

simplify60.0ms

Counts: 1 → 1

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
46.0ms	(* K (+ m n))
80.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series836.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
47.0ms	(* K (+ m n))
371.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
90.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify105.0ms

Counts: 89 → 89

prune530.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

1.4s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
70.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series743.0ms

Counts

2 → 6

Calls

2 calls:

285.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
458.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify64.0ms

Counts: 50 → 50

prune260.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(* (cbrt (+ m n)) (cbrt (+ m n)))
36.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite478.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`cos-sum` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

6.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
55.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
409.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series772.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (+ m n))
185.0ms	(cbrt (+ m n))
212.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
183.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify81.0ms

Counts: 103 → 103

prune867.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize85.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))
35.9b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

rewrite835.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
16×	`*-un-lft-identity`
12×	`cbrt-div`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (cbrt (+ m n)))
10.0ms	(cbrt (cbrt (+ m n)))
9.0ms	(cbrt (cbrt (+ m n)))
807.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt (cbrt (+ m n)))
367.0ms	(cbrt (cbrt (+ m n)))
323.0ms	(cbrt (cbrt (+ m n)))
133.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

simplify117.0ms

Counts: 73 → 73

prune664.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes356.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify124.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	8099×	body	80	valid
619.0ms	136×	body	640	valid
131.0ms	111×	body	1280	valid
54.0ms	123×	body	320	valid
13.0ms	49×	body	160	valid
3.0ms	2×	body	2560	valid